Scaling Up Robust MDPs using Function Approximation

Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):181-189, 2014.

Abstract

We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handling uncertainty, can be solved using dynamic programming for small to medium sized problems. However, due to the "curse of dimensionality", MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approximate dynamic programming method based on a projected fixed point equation to approximately solve large scale robust MDPs. We show that the proposed method provably succeeds under certain technical conditions, and demonstrate its effectiveness through simulation of an option pricing problem. To the best of our knowledge, this is the first attempt to scale up the robust MDP paradigm.

Related Material

@InProceedings{pmlr-v32-tamar14,
title = {Scaling Up Robust MDPs using Function Approximation},
author = {Aviv Tamar and Shie Mannor and Huan Xu},
booktitle = {Proceedings of the 31st International Conference on Machine Learning},
pages = {181--189},
year = {2014},
editor = {Eric P. Xing and Tony Jebara},
volume = {32},
number = {2},
series = {Proceedings of Machine Learning Research},
address = {Bejing, China},
month = {22--24 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v32/tamar14.pdf},
url = {http://proceedings.mlr.press/v32/tamar14.html},
abstract = {We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handling uncertainty, can be solved using dynamic programming for small to medium sized problems. However, due to the "curse of dimensionality", MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approximate dynamic programming method based on a projected fixed point equation to approximately solve large scale robust MDPs. We show that the proposed method provably succeeds under certain technical conditions, and demonstrate its effectiveness through simulation of an option pricing problem. To the best of our knowledge, this is the first attempt to scale up the robust MDP paradigm.}
}

%0 Conference Paper
%T Scaling Up Robust MDPs using Function Approximation
%A Aviv Tamar
%A Shie Mannor
%A Huan Xu
%B Proceedings of the 31st International Conference on Machine Learning
%C Proceedings of Machine Learning Research
%D 2014
%E Eric P. Xing
%E Tony Jebara
%F pmlr-v32-tamar14
%I PMLR
%J Proceedings of Machine Learning Research
%P 181--189
%U http://proceedings.mlr.press
%V 32
%N 2
%W PMLR
%X We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handling uncertainty, can be solved using dynamic programming for small to medium sized problems. However, due to the "curse of dimensionality", MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approximate dynamic programming method based on a projected fixed point equation to approximately solve large scale robust MDPs. We show that the proposed method provably succeeds under certain technical conditions, and demonstrate its effectiveness through simulation of an option pricing problem. To the best of our knowledge, this is the first attempt to scale up the robust MDP paradigm.

TY - CPAPER
TI - Scaling Up Robust MDPs using Function Approximation
AU - Aviv Tamar
AU - Shie Mannor
AU - Huan Xu
BT - Proceedings of the 31st International Conference on Machine Learning
PY - 2014/01/27
DA - 2014/01/27
ED - Eric P. Xing
ED - Tony Jebara
ID - pmlr-v32-tamar14
PB - PMLR
SP - 181
DP - PMLR
EP - 189
L1 - http://proceedings.mlr.press/v32/tamar14.pdf
UR - http://proceedings.mlr.press/v32/tamar14.html
AB - We consider large-scale Markov decision processes (MDPs) with parameter uncertainty, under the robust MDP paradigm. Previous studies showed that robust MDPs, based on a minimax approach to handling uncertainty, can be solved using dynamic programming for small to medium sized problems. However, due to the "curse of dimensionality", MDPs that model real-life problems are typically prohibitively large for such approaches. In this work we employ a reinforcement learning approach to tackle this planning problem: we develop a robust approximate dynamic programming method based on a projected fixed point equation to approximately solve large scale robust MDPs. We show that the proposed method provably succeeds under certain technical conditions, and demonstrate its effectiveness through simulation of an option pricing problem. To the best of our knowledge, this is the first attempt to scale up the robust MDP paradigm.
ER -